No, because it was Australia in the wrong both times. The first time for not understanding the rules about what makes a legitimate catch and the second for doing something clearly against the spirit of the game. Also them acting so hard done by when they really got away with one with Smith's catch from Root earlier in the game was pretty funny when they pretty much had the game sewn up by then.
It just feels like Jonny Bairstow is such an easy target as well, if this happened to Stokes or Smith in the middle of a run chase then it would be viewed far more clearly as the desperate and cheap wicket that it was. The debate isn't really about whether Bairstow was sloppy, because he undoubtedly was.
Most England fans have been pretty critical of the way England have managed these two tests and admit they probably would have lost anyway due to their own mistakes, but it ruined what was otherwise an interesting spectacle. England would be absolutely hammered by all sides for the same piece of play and accused of desperation, but the fact that Australia are the superior teams kind of masks that fact. They are, unfortunately, the best athletes and the worst sportsmen simultaneously.